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A relational logic for higher-order programs

2017
*
Proceedings of the ACM on Programming Languages
*

We present

doi:10.1145/3110265
dblp:journals/pacmpl/AguirreBG0S17
fatcat:tt2j2f4lqvgjpmtya2lpkhqi7m
*a**logic*, called*Relational**Higher**Order**Logic*(RHOL),*for*proving*relational*properties of*a*simply typed λ-calculus with inductive types and recursive definitions. ... proofs in*higher*-*order**logic*. ... ACKNOWLEDGMENTS We thank the anonymous reviewers*for*their helpful and thoughtful comments. This article is based on research that has been supported, in part, by NSF under grant TWC-1565365. ...##
###
A Relational Logic for Higher-Order Programs
[article]

2017
*
arXiv
*
pre-print

We present

arXiv:1703.05042v1
fatcat:o6w2un7m3zfrndpj2lagsc7zom
*a**logic*, called*Relational**Higher**Order**Logic*(RHOL),*for*proving*relational*properties of*a*simply typed λ-calculus with inductive types and recursive definitions. ... In*a**higher*-*order*setting,*relational**program*verification can be achieved using*relational*refinement type systems,*a*form of refinement types where assertions have*a**relational*interpretation. ...*A**relational*modal*logic**for**higher*-*order*stateful ADTs. ...##
###
A relational logic for higher-order programs

2019
*
Journal of functional programming
*

We present

doi:10.1017/s0956796819000145
fatcat:yxlwrfjjevgpxmo5ulbie5gsn4
*a**logic*, called*relational**higher*-*order**logic*(RHOL),*for*proving*relational*properties of*a*simply typed λ-calculus with inductive types and recursive definitions. ... In*a**higher*-*order*setting,*relational**program*verification can be achieved using*relational*refinement type systems,*a*form of refinement types where assertions have*a**relational*interpretation. ...*A**relational*modal*logic**for**higher*-*order*stateful ADTs. ...##
###
A relational realizability model for higher-order stateful ADTs

2012
*
The Journal of Logic and Algebraic Programming
*

data types

doi:10.1016/j.jlap.2012.03.004
fatcat:laxrygwefvffjfllvckzobxydu
*Logical**relations*Local state Parametricity We present*a*realizability model*for*reasoning about contextual equivalence of*higher*-*order**programs*with impredicative polymorphism, recursive types ... , and*higher*-*order*mutable state. ... And we thank the anonymous referees*for*many valuable comments, ranging from typos to directions*for*future work. ...##
###
A confluent relational calculus for higher-order programming with constraints
[chapter]

*
Constraints in Computational Logics
*

The -calculus provides

doi:10.1007/bfb0016846
dblp:conf/ccl/NiehrenS94
fatcat:uuy6athywvba5koluxdrvvmy7q
*for*higherorder*relational**programming*with rst-*order*constraints, and subsumes*higher*-*order*functional*programming*as*a*special case. ... The -calculus provides*for**logical*variables but not*for*rst-*order*uni cation, which would amount to the integration of*a*tree constraint system. ... Introduction We present the -calculus,*a**relational*calculus parametrized by*a**logical*constraint system. The -calculus provides*for**higher*-*order**relational**programming*with rst-*order*constraints. ...##
###
Modular reasoning about concurrent higher-order imperative programs

2014
*
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '14
*

*Higher*-

*Order*Separation

*Logics*Instead of specifying

*a*

*program*by

*relating*it to another

*program*, we can specify

*programs*using

*program*

*logics*. ... I will consider both

*relational*models and

*program*

*logics*based on

*higher*-

*order*separation

*logic*. ...

##
###
Page 2045 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

From the introduction: “In this chapter, we develop the idea of

*higher*-*order**logic**programming*by utilizing*a**higher*-*order**logic*as the basis*for*computing. ... There are, of course, many choices*for*the*higher*-*order**logic*that might be used in such*a*study. ...##
###
Programming with Higher-Order Logic, by Dale Miller and Gopalan Nadathur, Cambridge University Press, 2012, Hardcover, ISBN-10:052187940X, xiv + 306 pp

2014
*
Theory and Practice of Logic Programming
*

It covers syntax, semantics, and pragmatics of

doi:10.1017/s1471068414000027
fatcat:fh5pyehajzazjm6ynvgvc6ojlq
*higher*-*order**logic**programming*in*a*systematic and easy-to-read manner that will be of great value as introduction and reference*for*students and researchers ... This book is concerned with the second form when the underlying*logic*is*higher*-*order**logic*. ... Much has happened since the initial development of*higher*-*order**logic**programming*. Andreoli discovered the general theory of focusing as*a*broad basis*for**logic**programming*. ...##
###
Higher-order aspects of logic programming
[chapter]

1994
*
Lecture Notes in Computer Science
*

Are

doi:10.1007/3-540-58025-5_63
fatcat:qdq44baxdzfudg3ieh47p62344
*higher*-*order*extensions to*logic**programming*needed? We answer this question in the negative by showing that*higher*-*order*features are already available in pure*logic**programming*. ... It is demonstrated that*higher*-*order*lambda calculus-based languages can be compositionally embedded in*logic**programming*languages preserving their semantics and abstraction facilities. ... The objective here seems to be not*higher*-*order**logic**programming*, but*logic**programming*over*higher*-*order*terms. ...##
###
Middle-Out Reasoning for Synthesis and Induction
[chapter]

1996
*
Automated Mathematical Induction
*

We propose

doi:10.1007/978-94-009-1675-3_4
fatcat:hlrfxol3oreppivyqvd5k7rzyy
*a*novel approach to automating the synthesis of*logic**programs*:*Logic**programs*are synthesized as*a*by-product of the planning of*a*veri cation proof. ... The approach is*a*two-level one: At the object level, we prove*program*veri cation conjectures in*a*sorted, rst-*order*theory. The conjectures are of the form 8args ????! : prog(args ????! ... Thus, what we do is closely*related*to proving the*higher*-*order*conjecture 9P: 8args ????! : P(args ????! ) $ spec(args ????! ) where P represents*a*pure*logic**program*. ...##
###
Higher-order constrained horn clauses for verification

2017
*
Proceedings of the ACM on Programming Languages
*

The idea is to express the problem of finding such

doi:10.1145/3158099
dblp:journals/pacmpl/BurnOR18
fatcat:ndnyxiljkvgudh7dh42gebv3he
*a**program*invariant*logically*, as*a*satisfiability problem*for*the following set of*higher*-*order*constrained Horn clauses: ∀xyz. z = x + y ⇒ Add x y z ... Full terms of use are available: Motivated by applications in automated verification of*higher*-*order*functional*programs*, we develop*a*notion of constrained Horn clauses in*higher*-*order**logic*and*a*decision ... Part of this research was done while visiting the Institute*for*Mathematical Sciences, National University of Singapore in 2016. ...##
###
Page 573 of Mathematical Reviews Vol. , Issue 93b
[page]

1993
*
Mathematical Reviews
*

The authors present four abstract

*programming*languages: first-*order*and*higher*-*order*positive Horn clauses, and first-*order*and*higher*-*order*versions of*a*new class of formulas called hereditary Harrop ...*For*example, first-*order*Horn clauses do not support modules, abstract data types or*higher*-*order*functions. ...##
###
The expressive power of stratified logic programs

1991
*
Information and Computation
*

Every stratgied

doi:10.1016/0890-5401(91)90059-b
fatcat:aexvileko5f55b2uvolbkueynu
*program*computes*a*Ai*relation*on N = (N, +, . ). As*a*result, fixpoint*logic*has strictly*higher*expressive power than stratified*logic**programs*on the integers. ... Fixpoint*logic*has*higher*expressive power than stratified*logic**programs*on finite structures over any vocabulary that has*a**relational*symbol of arity at least two. ...##
###
The relation between logic and functional languages: a survey

1986
*
The Journal of Logic Programming
*

Both languages are based on

doi:10.1016/0743-1066(86)90014-2
fatcat:kzu7tvyz2fajvlsl767fgczjfe
*a**higher*-*order*functional language. The relevance of*higher*-*order*features in*logic*languages will be discussed in Section 10. ... On the other hand, lazy evaluation is highly desirable, mainly in*a*functional-*relational**logic*language, in*order*to define nonstrict functions (and*relations*) and*for*stream-based*logic**programming*. ... Let us finally remark that*higher*-*order*features could play*a*very important role in*logic**programs*, in addition to what is relevant to*programming*in general. ...##
###
Higher-Order Constrained Horn Clauses and Refinement Types
[article]

2017
*
arXiv
*
pre-print

Motivated by applications in automated verification of

arXiv:1705.06216v2
fatcat:qc4rib7saragnbcnzshaxt4hpu
*higher*-*order*functional*programs*, we develop*a*notion of constrained Horn clauses in*higher*-*order**logic*and*a*decision problem concerning their satisfiability ... Following work in*higher*-*order**program*verification, we develop*a*refinement type system in*order*to reason about and automate the search*for*models. ... Research was partially completed while the second and third authors were visiting the Institute*for*Mathematical Sciences, National University of Singapore in 2016. ...
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